Information Technology Reference
In-Depth Information
observe may correspond to c
D
0:1. We refer to this phenomenon as the
diffusive
transport
of a substance. The substance, ink in this case, flows from regions of high
concentration to regions of low concentration. As in the heat conduction example,
the flow tends to smooth out variations. An example related to ink in water is that
of sugar in coffee: If the coffee is not stirred, the sugar will dissolve and the sugar
molecules will distribute throughout the coffee by diffusion.
2
Cooking spaghetti is
yet another example: The water molecules diffuse into the spaghetti strands and
make them thicker and more flexible.
Widely different physical problems, such as heat conduction in metals, dissolving
sugar in coffee, or cooking spaghetti can all be described by the same mathemat-
ical model. This is the great power of using mathematics to model the physical
world: Seemingly very different phenomena can be described by the same equa-
tions, and these equations can be solved in a single program, which then can be
used to simulate diverse physical phenomena.
7.1.3
Diffusion Versus Convection
Getting back to the problem of putting a cube a sugar in the coffee, one is often too
impatient to wait for the diffusion process to finish; it takes some time before the
sugar cube has dissolved and spread throughout the coffee. Normally, one grabs a
spoon and furthers the mixing by moving the spoon around in the coffee. From a
physical point of view, one creates a fluid flow in the coffee, and the sugar molecules
are then transported more efficiently with the aid of the flow. This accelerates the
mixing of sugar and coffee. Transport due to fluid flow is often called
convection
.
Transport due to diffusion only is much slower. Most transport processes in nature
and technology are a combination of convection and diffusion. For example, heat
distribution in a building makes use of ventilation systems, imposing fluid flows, to
make the transport of heat more efficient than if we only waited for diffusion to heat
the building.
A problem of particular interest in our times is the transport of pollution, e.g., the
depositing of some polluting substance in an ocean, a river, a lake, or the ground. In
the case of a lake at rest, the transport of pollution has great similarities to dropping
ink in water: Both are diffusion processes. However, in a river or in an ocean, the
transport of pollution due to fluid flow is essential, so convection contributes much
more than pure diffusion to the distribution of the pollution. In fact, one can neglect
diffusion in such transport phenomena.
Even when you put a sugar cube in a cup of coffee, or ink in water, the mixing
will be influenced by both diffusion and convection. The convection arises because
the sugar or ink introduces density differences in the fluid mixture. Light fluid flows
2
Dissolving a substance in a fluid may involve convection as well as diffusion, as explained in the
forthcoming section.
